一类具有脉冲接种与脉冲剔除的SIQR模型  

An SIQR mode with impulsive vaccination and impulsive elimination

作　　者：马艳丽[1] 张仲华[2] 刘家保[3] 丁健[1] MA Yanli;ZHANG Zhonghua;LIU Jiabao;DING Jian(General Education Department, Anhui Xinhua University, He f ei 230088, China;School of Sciences, Xi ＇ an University of Science and Technology, Xi ＇ an 710049, China;School of Sciences, Anhui Jianzhu University, Hefei 230601, China)

机构地区：[1]安徽新华学院通识教育部,安徽合肥230088 [2]西安科技大学理学院,陕西西安710049 [3]安徽建筑大学理学院,安徽合肥230601

出　　处：《中国科学技术大学学报》2018年第2期111-117,共7页JUSTC

基　　金：安徽省高校优秀青年人才支持计划项目(gxyq2017125);安徽省高校自然科学重点研究项目(KJ2016A310);安徽省教学研究项目(2016JYXM0481);安徽新华学院校级自然科学重点研究项目(2016zr003)资助

摘　　要：同时考虑了脉冲接种、脉冲剔除和隔离策略,建立了一个SIQR传染病模型,从理论分析和数值模拟方面研究了SIQR传染病模型的动力学性质.首先,得到了模型的无病周期T解的存在性和基本再生数R0;其次,应用Floquet定理证明了无病周期T解的局部渐近稳定性和利用脉冲微分不等式证明了其全局渐近稳定性;接着,进行了计算机数值模拟来进一步验证理论结果的正确性.最后,通过对基本再生数R0及其偏导数,分析了脉冲接种、脉冲剔除和隔离这些预防和控制策略对传染病流行的影响.Impulsive vaccination,impulsive elimination and quarantine strategies were considered in an SIQR epidemic model.The dynamical behavior of an SIQR epidemic model was discussed both theoretically and numerically.Firstly,the disease-free T periodic solution and the basic reproductive number R0 were obtained.Secondly,the local asymptotic stability of the disease-free T periodic solution with Floquet theorem was proved and the global asymptotic stability of the disease-free T periodic solution was also proved by impulsive differential equation.Thirdly,numerical simulation was conducted to illustrate the theoretical analysis.Finally,the influence of impulsive vaccination,impulsive elimination and quarantine strategies for epidemics was analyzed by the expression of the basic reproductive number R0 and its partial derivative.

关 键 词：传染病模型 基本再生数 全局渐近稳定性 脉冲微分方程 脉冲接种 脉冲剔除 

分 类 号：O175[理学—数学]